A pair of fire towers uses technology to search for forest
fires. Let the center of the forest be the origin on a
coordinate grid. The first fire tower is located 5 km east
and 8 km south of the center, and the second fire tower
is located 7 km west and 4 km north of the center. The
technology at the first tower can locate fires within a
radius of 10 km and the second tower within a radius of
9 km. The system of inequalities represents this
scenario.
[(x-5)² + (y+8)² ≤ 100
(x+7)²+(y-4)² ≤81
At which location, from the origin, would a fire be
detected by both towers?
2 km east and 3 km south
3 km east and 2 km north
2 km west and 1 km north
1 km west and 2 km south
